A Post-Design of Topology Optimization for Mechanical Compliant Amplifier in MEMS

[[abstract]]The topology synthesis approach can generate a creative initial optimized configuration and can generate approximately well locations of hinges. It is particularly useful to form a monolithic compliant mechanism in MEMS application. However, the formation of hinges-like portion is typically encountered as a major unsolved problem. Such hinges unavoidably exist in the topological layout but cannot practically manufacture. This paper proposes an approach using the analytic single-axis flexure hinge integrated with the formal optimization as a post-design process to obtain optimum flexure hinges and its location for promoting the overall performance. A compliant micro gripper/magnifying mechanism is adopted as an example to illustrate the presenting approach; and a multi-objective optimization problem consisting of several constraints are constructed to determine nine unknowns. The numerical experiment shows the proposed post-optimum design is effective and can be utilized to other similar design situation.[[incitationindex]]E

Minimum length-scale constraints for parameterized implicit function based topology optimization

Open access via Springer Compact Agreement The author would like to thank the Numerical Analysis Group at the Rutherford Appleton Laboratory for their FORTRAN HSL packages (HSL, a collection of Fortran codes for large-scale scientific computation. See http://www.hsl.rl.ac.uk/). The author also would like to acknowledge the support of the Maxwell compute cluster funded by the University of Aberdeen. Finally, the author thanks the anonymous reviewers for their helpful comments and suggestions that improved this paper.Peer reviewedPublisher PD

On Advancing the Topology Optimization Technique to Compliant Mechanisms and Robots

Compliant mechanisms (CMs) take advantage of the deformation of their flexible members to transfer motion, force, or energy, offering attractive advantages in terms of manufacturing and performance over traditional rigid-body mechanisms (RBMs). This dissertation aims to advance the topology optimization (TO) technique (1) to design CMs that are more effective in performing their functions while being sufficiently strong to resist yield or fatigue failure; and (2) to design CMs from the perspective of mechanisms rather than that of structures, particularly with the insight into the concepts of joints, actuations, and functions of mechanisms. The existing TO frameworks generally result in CMs that are much like load-bearing structures, limiting the applications of CMs. These CMs (1) do not have joints, (2) are actuated by a translational force, and (3) can only do simple work such as amplifying motion or gripping. Three TO frameworks for the synthesis of CMs are proposed in this dissertation and they are summarized below. First, a framework was developed for the design of efficient and strong CMs. The widely used stiffness-flexibility criterion for CM design with TO results in lumped CMs that are intrinsically efficient in transferring motion, force, or energy but are prone to high localized stress and thus weak to resist yield or fatigue failure. Indeed, distributed CMs may have a better stress distribution than lumped CMs but have the weakness of being less efficient in motion, force, or energy transfer than lumped CMs. Based on this observation, the proposed framework rendered the concept of hybrid systems, hybrid CMs in this case. Further, the hybridization was achieved by a proposed super flexure hinge element and a design criterion called input stroke criterion in addition to the traditional stiffness-flexibility criterion. Both theoretical exploration and CM design examples are presented to show the effectiveness of the proposed approach. The proposed framework has two main contributions to the field of CMs: (1) a new design philosophy, i.e., hybrid CMs through TO techniques and (2) a new design criterion—input stroke. Second, a systematic framework was developed for the integrated design of CMs and actuators for the motion generation task. Both rotary actuators and bending actuators were considered. The approach can simultaneously synthesize the optimal structural topology and actuator placement for the desired position, orientation, and shape of the target link in the system while satisfying the constraints such as buckling constraint, yield stress constraint and valid connectivity constraint. A geometrically nonlinear finite element analysis was performed for CMs driven by a bending actuator and CMs driven by a rotary actuator. Novel parameterization schemes were developed to represent the placements of both types of actuators. A new valid connectivity scheme was also developed to check whether a design has valid connectivity among regions of interest based on the concept of directed graphs. Three design examples were constructed and a compliant finger was designed and fabricated. The results demonstrated that the proposed approach is able to simultaneously determine the structure of a CM and the optimal locations of actuators, either a bending actuator or a rotary actuator, to guide a flexible link into desired configurations. Third, the concept of a module view of mechanisms was proposed to represent RBMs and CMs in a general way, particularly using five basic modules: compliant link, rigid link, pin joint, compliant joint, and rigid joint; this concept was further developed for the unified synthesis of the two types of mechanisms, and the synthesis approach was thus coined as module optimization technique—a generalization of TO. Based on the hinge element in the finite element approach developed at TU Delft (Netherlands in early 1970), a beam-hinge model was proposed to describe the connection among modules, which result in a finite element model for both RBMs and CMs. Then, the concept of TO was borrowed to module optimization, particularly to determine the “stay” or “leave” of modules that mesh a design domain. The salient merits with the hinge element include (1) a natural way to describe various types of connections between two elements or modules and (2) a provision of the possibility to specify the rotational input and output motion as a design problem. Several examples were constructed to demonstrate that one may obtain a RBM, or a partially CM, or a fully CM for a given mechanical task using the module optimization approach

Topology optimization of compliant mechanisms based on the BESO method

This dissertation explores topology optimization techniques for designing compliant mechanisms actuated by forces. For a compliant mechanism, it has the potential of reducing part count, mechanical joints, operation noise, and manufacturing and assembly costs over a traditional rigid-link mechanism. Thus the application of compliant mechanisms is becoming increasingly prevalent in medical instruments and mechanical devices. Optimization of compliant mechanisms has drawn intense attention of many researchers. However, this design field has been facing many challenges and shortages in several aspects such as optimization method, optimization algorithm and resulting topology. For example, convergence problems often lead to vague solutions. Optimization algorithms are not very suitable to investigate the real physical significance. Furthermore, designs of compliant mechanisms using topology optimization techniques naturally lead to the introduction of hinges into final topologies. In addition, the previous design also focuses mainly on the optimal design of linear compliant mechanisms. In fact, optimizing nonlinear compliant mechanisms is proving quite necessary in real applications as the simulation is more accurate. Therefore, it is important to devote efforts to the modification of previous optimization techniques for constructing practical compliant mechanism designs. This dissertation proposes a modified bi-directional evolutionary structural optimization (BESO) method for the optimal design of linear and geometrically nonlinear compliant mechanisms. Numerical algorithms based on the BESO method are developed through various objectives and constraints in compliant mechanism design. Firstly, to consider functional behaviours of compliant mechanisms, sets of clear and suitable structural configurations are produced by quantifying various performance characteristics and changing the stiffness of attached springs. This implies that material distribution and hinge formation are demonstrated in this work. To achieve prescribed structural stiffness for optimized mechanisms, a new BESO algorithm is established for solving the proposed optimization problem by gradually updating design variables. The inverter and the gripper optimization problems serve to demonstrate the practicability and effectiveness of the proposed method. Besides this, a new formulation is established by considering desirable deformation and simultaneously precluding the formation of hinges in order to design hinge-free compliant mechanisms, verified by a large number of numerical experiments including rare 3D hinge-free designs. Furthermore, compliant mechanisms often undergo large displacement, in order to provide their functionality. Therefore, the research also addresses the optimal design of compliant mechanism with geometrically nonlinear behaviours. With the aid of the hard-kill BESO method, a new systemic design approach is developed to overcome the convergence difficulty caused by extreme deformation in the nonlinear finite element analysis. Large-displacement inverter design with the desired structural stiffness is provided based on a new evolutionary optimization technique involved in a developed multi-criteria flexibility-stiffness formulation. Overall, the modified BESO method has effectively set up new optimizations, visualizing and analysing the resulting topologies for 2D and 3D compliant mechanism designs. The findings shown in this dissertation have also established appropriate techniques for designing various linear compliant mechanisms. In addition, an efficient and robust methodology has been provided for the topology optimization of geometrically nonlinear compliant mechanisms. Furthermore, the work has provided a solid foundation for creating a practical design tool in the form of a user-friendly computer program, which is suitable for the conceptual design of a wide range of compliant mechanisms

Topology optimization of compliant mechanisms using element-free Galerkin method

© 2015 Elsevier Ltd. All rights reserved. This paper will propose a topology optimization approach for the design of large displacement compliant mechanisms with geometrical non-linearity by using the element-free Galerkin (EFG) method. In this method, the Shepard function is applied to construct a physically meaningful density approximant, to account for its non-negative and range-bounded property. Firstly, in terms of the original nodal density field, the Shepard function method functionally similar to a density filter is used to generate a non-local nodal density field with enriched smoothness over the design domain. The density of any node can be evaluated according to the nodal density variables located inside the influence domain of the interested node. Secondly, in the numerical implementation the Shepard function method is again employed to construct a point-wise density interpolant. Gauss quadrature is used to calculate the integration of background cells numerically, and the artificial densities over all Gauss points can be determined by the surrounding nodal densities within the influence domain of the concerned computational point. Finally, the moving least squares (MLS) method is applied to construct the shape functions using the weight functions with compact support for assembling the meshless approximations of state equations. Since MLS shape functions are lack of the Kronecker delta function property, the penalty method is applied to enforce the essential boundary conditions. A typical large-deformation compliant mechanism is used as the numerical example to demonstrate the effectiveness of the proposed method

Multiple-Material Topology Optimization of Compliant Mechanisms Created via Polyjet 3D Printing

Compliant mechanisms are able to transfer motion, force, and energy using a monolithic structure without discrete hinge elements. The geometric design freedoms and multi-material capability offered by the PolyJet 3D printing process enables the fabrication of compliant mechanisms with optimized topology. The inclusion of multiple materials in the topology optimization process has the potential to eliminate the narrow, weak, hinge-like sections that are often present in single-material compliant mechanisms. In this paper, the authors propose a design and fabrication process for the realization of 3-phase, multiple-material compliant mechanisms. The process is tested on a 2D compliant force inverter. Experimental and theoretical performance of the resulting 3-phase inverter is compared against a standard 2-phase design.Mechanical Engineerin

Compliant mechanisms design with fatigue strength control: a computational framework

A compliant mechanism gains its motion from the deflection of flexible members or the deformation of one portion of materials with respect to other portions. Design and operation of compliant mechanisms are very important, as most of the natural objects are made of compliant materials mixed with rigid materials, such as the bird wings. The most serious problem with compliant mechanisms is their fatigue problem due to repeating deformation of materials in compliant mechanisms. This thesis presents a study on the computational framework for designing a compliant mechanism under fatigue strength control. The framework is based on the topology optimization technique especially ground structure approach (GSA) together with the Genetic Algorithm (GA) technique. The study presented in this thesis has led to the following conclusions: (1) It is feasible to incorporate fatigue strength control especially the stress-life method in the computational framework based on the GSA for designing compliant mechanisms and (2) The computer program can well implement the computational framework along with the general optimization model and the GA to solve the model. There are two main contributions resulting from this thesis: First one is provision of a computational model to design compliant mechanisms under fatigue strength control. This model also results in a minimum number of elements of the compliant mechanism in design, which means the least weight of mechanisms and least amount of materials. Second one is an experiment for the feasibility of implementing the model in the MATLAB environment which is widely used for engineering computation, which implies a wide applicability of the design system developed in this thesis

Topology optimization of 3D compliant actuators by a sequential element rejection and admission method

This work presents a sequential element rejection and admission (SERA) method for optimum topology design of three dimensional compliant actuators. The proposed procedure has been successfully applied to several topology optimization problems, but most investigations for compliant devices design have been focused on planar systems. This investigation aims to progress on this line, where a generalization of the method for three dimensional topology optimization is explored. The methodology described in this work is useful for the synthesis of high performance flexure based micro and nano manipulation applications demanding for both sensing and control of motion and force trajectories. In this case the goal of the topology optimization problem is to design an actuator that transfers work from the input point to the output port in a structurally efficient way. Here we will use the classical formulation where the displacement performed on a work piece modelled by a spring is maximized. The technique implemented works with two separate criteria for the rejection and admission of elements to efficiently achieve the optimum design and overcomes problems encountered by other evolutionary methods when dealing with compliant mechanisms design. The use of the algorithm is demonstrated through several numerical examples